Problem: Rewrite as a simplified fraction. ${0.5\overline{97} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 597.9797...\\ 10x &= 5.9797...\end{align*}}$ Subtracting the two equations, we have: ${990x = 592}$ ${x = \dfrac{592}{990}} $ ${x = \dfrac{296}{495}} $